Abstract:The goal of this paper is to investigate outage performance in a multi-spectral bi-directional full-duplex system (M-BFD). The system considered is two-way communication between two nodes equipped with a single shared antenna. Because full-duplex transmission is being employed, the required SNR associated with the target rate at each node for BFD is smaller than that for a bi-directional half-duplex system (BHD). In a single spectrum environment, therefore, BFD outperforms BHD in terms of outage probability. From a practical perspective, we investigate whether BFD remains advantageous over BHD in a multi-spectrum environment. We investigate the optimal spectrum selection strategy in terms of outage probability for M-BFD. The outage probability is derived as a closed-form expression under this selection strategy. The results show that the diversity orders for M-BFD and multi-spectral BHD (M-BHD) are identical. In the high signal-to-noise ratio (SNR) range, furthermore, the SNR difference between the outage curves for M-BFD and for M-BHD is shown to be inversely proportional to the number of available spectra, but in proportional to the target data rate.